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Updated: Dec 8, 2025
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Self-assembling Morphologies Obtained from Helical Polycarbodiimide Copolymers and Their Triazole Derivatives
Published on: February 7, 2017
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Geodesic fibrations for packing diabolic domains.
Randall D Kamien1,2, Thomas Machon3
1Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104.
Summary
We present a theory for packing hyperboloid domains in liquid crystal textures, creating novel bend-free structures. These structures exhibit unique properties, including energy reduction and shock-wave-like defects.
Area of Science:
- Physics
- Materials Science
- Geometry
Background:
- Liquid crystals exhibit complex textures with potential applications.
- Understanding domain packing is crucial for controlling material properties.
Purpose of the Study:
- To develop a theory for packing hyperboloid "diabolic" domains in bend-free liquid crystal textures.
- To explore the resulting textures, their energy, and potential phases.
Main Methods:
- Theoretical modeling of domain packing.
- Analysis of domain relationships via Lorentz transformations.
- Geometric exploration relating textures to Milnor fibrations.
Main Results:
- Continuous packing of diabolic domains creates diverse bend-free textures.
- Lorentz transformations can reduce system elastic energy.
- New phases, including splay-twist analogues of blue phases, are predicted.
- Defects analogous to shock waves can arise from "superluminal boosts."
- Textures are geometrically linked to Milnor fibrations of the Hopf link.
Conclusions:
- A unified theory for diabolic domains exists in four-dimensional space.
- This work provides a framework for designing novel liquid crystal materials with tunable properties.
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